Noncommutative geometry inspired AdS black hole with a cloud of strings surrounded by quintessence-like fluid

Abstract We investigate the geometric and physical properties of an anti-de Sitter (AdS) black hole (BH) space-time coupled by a cloud of strings (CoS) and surrounded by a quintessence-like fluid (QF), all within the framework of non-commutative (NC) geometry. From the perspective of geometrical optics, we analyze the behavior of null geodesics, focusing on key optical features such as the effective potential, the structure and radius of the photon sphere, photon trajectories, and the resulting BH shadow. Our findings show that the combined effects of CoS and QF significantly modify photon dynamics and optical observables, leading to notable deviations from standard BH scenarios in NC geometry background. We also examine time-like geodesics, with particular emphasis on the innermost stable circular orbits (ISCOs). The results demonstrate that the presence of geometric and physical parameters alters the ISCO radius compared to conventional solutions. In addition, we explore the thermodynamic behavior of the BH solution, deriving key expressions, such as the Hawking temperature, entropy, Gibbs free energy, and specific heat capacity. The factors CoS and QF introduces substantial modifications to the thermodynamic profile, including shifts in phase transition points and changes to stability conditions under NC geometric effects. Furthermore, we study the dynamics of massless scalar field perturbations in this modified background by formulating the Klein–Gordon equation and reducing it to a Schrödinger-like form via separation of variables. The effective potential shows how CoS and QF shape perturbations in NC geometry background. Finally, we compute the quasinormal modes (QNMs) spectra by varying these parameters using the WKB method.